Differential Equations: Linear vs. Nonlinear

It is usually extremely difficult to solve a nonlinear differential equation A[u]=0 directly but it may be much easier to discover the minimum or maximum points of an appropriate energy functional I(u) where A=I’.
Such variational principle is advocated by Max Plank as a fundamental law in nature (e.g., relativity theory follows a geodesic path derived [...]

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Heisenberg’s Uncertainty Principle

I have personally come across this famour Heisenberg’s Uncertainty Principle many times in my lifetime – when I was a college student, when I started to learn about what is short-time FT, when I prepared my courses on wavelet. I must admit it is a difficult concept to grasp and I often adopt the strategy [...]

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Tips for my students (I)

1. Be more selective on reading papers and books. The game of scientific research is a constrained optimization problem – maximize your productivity (in terms of both quality and quantity) subject to certain time constraint. This time constraint simply dictates that you need to more carefully think about how you want to spend your time. [...]

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MATLAB Session (II)

1. How to improve the efficiency of your MATLAB program? 1) Vectorizing your codes: get familiar with functions such as all, end, repmat, squeeze, any, find, reshape, sub2ind, ind2sub, permute, shiftdim, sum, diff, ipermute, prod, sort; 2) Avoid frequent file I/O: if you have to store/retrieve some intermediate results, use save/load instead fwrite/fread because load [...]

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Tips related to MATLAB-based image processing

This blog contains some tips I shared with the students taking my EE465 (undergraduate image processing class). The objective of the lecture is to use circle detection (an elementary image analysis problem) as an example of demonstrating how to make a better use of MATLAB to solve image processing problems:
1. Master the language – enrich [...]

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